WIP

poc/example_flp_shamir.py

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+'''
+Demonstration of FLP functionality over Shamir secret shares.
+'''
+
+from typing import TypeVar
+from unittest import TestCase
+
+from vdaf_poc.common import vec_add
+from vdaf_poc.field import Field, Field64, poly_interp
+from vdaf_poc.flp_bbcggi19 import Sum
+
+F = TypeVar("F", bound=Field)
+
+def shamir_shard(field: type[F],
+                 meas: list[F],
+                 unshard_threshold: int,
+                 num_shares: int) -> list[list[F]]:
+    '''
+    Compute Shamir's threshold secret sharing of `meas`. `num_shares` specifies
+    the total of number of shares; `unshard_threshold` specifies the number of
+    shares needed to unshard.
+    '''
+    # NOTE It would be more efficient to do "packed" Shamir by letting f(x) =
+    # meas + rand_1 * x + rand_2 * x^2 + ..., and so on and letting the shares
+    # be f(0), f(1), ..., and so on. That is:
+    #
+    # coeffs = [meas]
+    # for _ in range(unshard_threshold):
+    #    coeffs.append(field.rand_vec(len(meas)))
+    #
+    # meas_shares = []
+    # for x in range(num_shares):
+    #     f = field.zeros(len(meas))
+    #     for (i, c) in enumerate(coeffs):
+    #         for j in range(len(meas)):
+    #             f[j] += c[j] * field(x)**i
+    #     meas_shares.append(f)
+    #
+    # However we would need a version of `poly_interp()` that operates on
+    # vectors over the field.
+    meas_shares = [field.zeros(len(meas)) for _ in range(num_shares)]
+    for i in range(len(meas)):
+        coeffs = [meas[i]] + field.rand_vec(unshard_threshold-1)
+        for j in range(num_shares):
+            f = field(0)
+            for (k, c) in enumerate(coeffs):
+                x = field(j+1)
+                f += c * x ** k
+            meas_shares[j][i] = f
+    return meas_shares
+
+def shamir_unshard(field: type[F],
+                   index: list[int],
+                   meas_shares: list[list[F]]) -> list[F]:
+    '''
+    Combine Shamir secret shares `meas_share` into the underlying secret.
+    `index` is indicates the index of each secret share. That is, `index[I]` is
+    equal to the index of `meas_share[I]` in the output of `shamir_shard()`.
+    '''
+    meas_len = len(meas_shares[0])
+    meas = []
+    for i in range(meas_len):
+        xs = []
+        fs = []
+        for (j, share) in zip(index, meas_shares):
+            x = field(j+1)
+            f = share[i]
+            xs.append(x)
+            fs.append(f)
+        coeffs = poly_interp(field, xs, fs)
+        meas.append(coeffs[0])
+    return meas
+
+
+class TestShamir(TestCase):
+    def test_shard_unshard(self) -> None:
+        '''Test the basic functionality.'''
+        meas = [Field64(13), Field64(37)]
+        meas_shares = shamir_shard(Field64, meas, 2, 3)
+        got = shamir_unshard(Field64, [0, 1], [meas_shares[0], meas_shares[1]])
+        self.assertEqual(got, meas)
+        got = shamir_unshard(Field64, [0, 2], [meas_shares[0], meas_shares[2]])
+        self.assertEqual(got, meas)
+        got = shamir_unshard(Field64, [1, 2], [meas_shares[1], meas_shares[2]])
+        self.assertEqual(got, meas)
+
+    def test_aggregate(self) -> None:
+        '''Show that Shamir secret sharing works with aggregation as well.'''
+        unshard_threshold = 2
+        num_shares = 3
+        max_measurement = 100
+        v = Sum(Field64, max_measurement)
+        agg_shares = [v.field.zeros(v.OUTPUT_LEN)] * num_shares
+        for x in range(max_measurement):
+            meas = v.encode(x)
+            meas_shares = shamir_shard(v.field,
+                                       meas,
+                                       unshard_threshold,
+                                       num_shares)
+            for j in range(num_shares):
+                agg_shares[j] = vec_add(agg_shares[j], v.truncate(meas_shares[j]))
+        agg = shamir_unshard(v.field, [0,1], [agg_shares[0], agg_shares[1]])
+        agg_result = v.decode(agg, max_measurement)
+        self.assertEqual(agg_result, max_measurement * (max_measurement-1) / 2)
+
+
+